Gaussianity Measures for Detecting the Direction of Causal Time Series

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The Arrow of Time in Multivariate Time Series (2016, background): “Hern´andez-Lobato et al. (2011), Morales-Mombiela et al. (2013) and Hern´andez-Lobato et al. (2014) discuss the derivation and application of Gaussianity measures to detect the direction of causal time series.”
Non-linear Causal Inference using Gaussianity Measures (2014, methodology): “In their work, Hernández-Lobato et al. (2011) show some advantages of using statistical tests based on measures of Gaussianity to determine the temporal direction of a time series, as a practical alternative to statistical tests based on the independence of the cause and the residual.”
Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence Statistical Tests for the Detection of the Arrow of Time in Vector Autoregressive Models (unknown): “…t = φX t−1 + t , , t ⊥ X t−1 , (2) with non-Gaussian i.i.d noise t , the residuals of a linear model in the backward time directioñ t ≡ X t − φX t+1 , t = 1, 2, . . . , T , (3) are more Gaussian than the corresponding residuals in the forward direction, { t } T t=1 [Hernández-Lobato et al., 2011] .”